I'm just gonna focus on one thing you mentioned here. Regardless of what you actually meant in total, the mere use of the idea of "insulated from costs" is a bit of a null argument, both logically and empirically. People are -already- disconnected from their healthcare costs. If you're sick, especially life-threateningly sick but also livelihood-threateningly and just plain "I don't want to be sick", then people don't tend to try and haggle.
Healthcare providers have you by the pursestrings, basically. It's hard to haggle for something you -need to survive-, -right now-. Food can be haggled because, even though you need it to survive, you're buying food to use in the future, so you have time to go to another, cheaper place. Health care, you either get fixed now or you die. At least for the life-threatening stuff.
That's why having a united front to negotiate with healthcare companies is good. Health insurance sounds like it could do that, a united group of people behind the insurance company who negotiates for them, but with a profit motive behind it, that doesn't work out. The insurer can negotiate cheaper prices from providers, then pocket the money instead of passing the savings onto the consumer. A government is better in that regard because, not only is there little-to-no profit motive, but they negotiate for the entire populace. More competition in that case, in a safe manner.
And empirically, a public health care system is pretty much the epitome of "insulated from costs", since you pay the same amount in taxes no matter how much of it you use. With insurance, you decide "Do I want this much coverage or that much?", which is sight more cost-weighing than "Eh, I'm sick, I'll go to the clinic." And in those countries with such a healthcare system, not only is it cheaper per capita for both public costs and private, but Americans pay more public costs for healthcare per capita than other countries pay per capita at all, both public and private. Then you add on the American private health costs and the American costs doubles. All for a country with mediocre-at-best health care, downright appalling at worst.